Electron configuration





In Chemistry electron configuration is the term used to refer to the
arrangement of electrons within an atom.

Since electrons are fermions they are subject to the Pauli exclusion
principle, which states that no two fermions can occupy the same state at
once. This is the fundamental basis of the configuration of electrons in an
atom: once a state is occupied by an electron, the next electron must occupy
a different quantum mechanical state.

In an atom, the stationary states of an electron's wavefunction (i.e. the
states which are eigenstates of the Schršdinger equation HΨ = EΨ
where H is the Hamiltonian) are referred to as orbitals, by analogy with the
classical picture of electron particles orbiting the nucleus. These states
have four principal quantum numbers: n, l, ml and ms, and by the Pauli
principle no two electrons may share the same values for all four numbers.
The two most important of these are n and l.

The first quantum number n corresponds to the overall energy and hence also
the distance from the nucleus of an orbital, hence sets of states with the
same n are often referred to as electron shells or energy levels. These are
not sharply delineated zones within the atom, but rather fuzzy-edged regions
within which an electron is likely to be found, due to the probabilistic
nature of quantum mechanical wavefunctions.

The second quantum number l corresponds to the angular momentum of the
state. These states take the form of spherical harmonics, and so are
described by Legendre polynomials. The different states relating to
different values of l are sometimes called sub-shells, and (mainly for
historical reasons) are referred to by letter, as follows:

 l value Letter  Maximum number of electrons in shell

 0       s       2

 1       p       6

 2       d       10

 3       f       14

 4       g       18

Each of the different angular momentum states can take 2(2l+1) electrons.
This is because the third quantum number ml (which can be thought of
[somewhat inaccurately] as the [quantised] projection of the angular
momentum vector on the z-axis) runs from -l to l in integer units, and so
there are 2l+1 possible states. Each distinct nlml state can be occupied by
two electrons with opposing spins (given by the quantum number ms), giving
2(2l+1) electrons overall. States with higher l than given in the table are
perfectly permissible in theory, but these values cover all atoms so far
discovered.

For a given value of n the possible values of l range from 0 to n-1;
therefore, the n=1 shell only possesses an s subshell and can only take 2
electrons, the n=2 shell possesses an s and a p subshell and can take 8
electrons overall, the n=3 shell possesses s, p and d subshells and has a
maximum of 18 electrons, and so on (generally speaking, the maximum number
of electrons in the nth energy level is 2n2).

In the ground state of an atom, the states are "filled" in order of
increasing energy; i.e., the first electron goes into the lowest energy
state, the second into the next lowest, and so on. The fact that the 3d
state is higher in energy than the 4s state but lower than the 4p is the
reason for the existence of the transition metals. The order in which the
states are filled is as follows:

 1s
 2s           2p
 3s           3p
 4s        3d 4p
 5s        4d 5p
 6s     4f 5d 6p
 7s     5f 6d 7p
 8s  5g 6f 7d 8p
 ...

This leads directly to the structure of the periodic table. The chemical
properties of an atom are largely determined by the arrangement of the
electrons in its outermost ("valence") shell (although other factors, such
as atomic radius, atomic mass, and increased accessibility of additional
electronic states also contribute to the chemistry of the elements as atomic
size increases).

Progressing through a group from lightest element to heaviest element, the
outer-shell electrons (those most readily accessible for participation in
chemical reactions) are all in the same type of orbital, with a similar
shape, but with increasingly higher energy and average distance from the
nucleus. For instance, the outer-shell (or "valence") electrons of the first
group, headed by hydrogen all have one electron in an s orbital. In
hydrogen, that s orbital is in the lowest possible energy state of any atom,
the first-shell orbital (and represented by hydrogen's position in the first
period of the table). In francium, the heaviest element of the group, the
outer-shell electron is in the seventh-shell orbital, significantly further
out on average from the nucleus than those electrons filling all the shells
below it in energy. As another example, both carbon and lead have four
electrons in their outer shell orbitals.

Because of the importance of the outermost shell, the different regions of
the periodic table are sometimes referred to as periodic table blocks, named
according to the sub-shell in which the "last" electron resides, e.g. the
s-block, the p-block, the d-block, etc.

An example of the notation commonly used to give the electron configuration
of an atom, in this case silicon (atomic number 14), is as follows: 1s2 2s2
2p6 3s2 3p2 The numbers are the shell number, n; the letters refer to the
angular momentum state, as given above, and the superscripted numbers are
the number of electrons in that state for the atom in question. An even
simpler version is simply to quote the number of electrons in each shell, eg
(again for Si): 2-8-4.

In molecules, the situation becomes much more complex: see molecular
orbitals for details. Similar, but not identical, arguments can be applied
to the protons and neutrons in the atomic nucleus: see the shell model of
nuclear physics.